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Salinon

Age 14 to 16 Challenge Level:

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

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Salt's Mill

Age 14 to 16 Short Challenge Level:

A window frame in Salt's Mill consists of two equal semicircles and a circle inside a large semicircle. What is the radius of the circle?

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Sam Again

Age 11 to 14 Challenge Level:

Here is a collection of puzzles about Sam's shop sent in by club members. Perhaps you can make up more puzzles, find formulas or find general methods.

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Sam's Quick Sum

Age 7 to 11 Challenge Level:

What is the sum of all the three digit whole numbers?

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Same Answer

Age 11 to 14 Challenge Level:

Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?

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Same Face

Age 11 to 14 Short Challenge Level:

A cube is rolled on a plane, landing on the squares in the order shown. Which two positions had the same face of the cube touching the surface?

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Same Height

Age 14 to 16 Challenge Level:

A trapezium is divided into four triangles by its diagonals. Can you work out the area of the trapezium?

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Same Length

Age 11 to 16 Challenge Level:

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

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Same Length Trains

Age 5 to 7 Challenge Level:

How many trains can you make which are the same length as Matt's, using rods that are identical?

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Same Number!

Age 14 to 16 Challenge Level:

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

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Same or Different?

Age 7 to 11 Challenge Level:

Anna and Becky put one purple cube and two yellow cubes into a bag to play a game. Is the game fair? Explain your answer.

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Same Shapes

Age 5 to 7 Challenge Level:

How can these shapes be cut in half to make two shapes the same shape and size? Can you find more than one way to do it?

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Sample

Age 14 to 16 Short Challenge Level:

Can you match the samples to the populations?

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Sampling and Hypothesis Testing

Age 16 to 18

Resources to support an advanced course of statistics

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Sangaku

Age 16 to 18 Challenge Level:

The square ABCD is split into three triangles by the lines BP and CP. Find the radii of the three inscribed circles to these triangles as P moves on AD.

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Satisfying Four Statements

Age 7 to 11 Challenge Level:

Can you find any two-digit numbers that satisfy all of these statements?

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Satisfying Statements

Age 11 to 14 Challenge Level:

Can you find any two-digit numbers that satisfy all of these statements?

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Satnav Dilemma

Age 11 to 14 Short Challenge Level:

How many routes are there in this diagram from S to T?

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Saying What You See - Lower Primary

You and your friends are probably quite good at imagining things and seeing things in lots of different ways. Here you'll put that to use in doing some maths challenges.

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Saying What You See - Upper Primary

You and your friends are probably quite good at imagining things and seeing things in lots of different ways. Here you'll put that to use in doing some maths challenges.

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Scale and Measurement

Age 11 to 16

Without scale and measurement, science, design and engineering would not exist!

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Scale Draw

Age 5 to 7 Challenge Level:

Use the grids to draw pictures to different scales.

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Scale Invariance

Age 16 to 18 Challenge Level:

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

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Scalene Area

Age 11 to 14 Short Challenge Level:

Can you find the area of this scalene triangle?

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Scaling

The Scaling collection of STEM resources

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Scaling Clowns

Age 5 to 7 Challenge Level:

These five clowns work in pairs. What is the same and what is different about each pair's faces?

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Scaling up and Down

Age 7 to 11

These activities are all about scaling different amounts up or down.

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Scheduling

The Scheduling collection of STEM resources

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Schlafli Tessellations

Age 11 to 18 Challenge Level:

are somewhat mundane they do pose a demanding challenge in terms of 'elegant' LOGO procedures. This problem considers the eight semi-regular tessellations which pose a demanding challenge in terms of. . . .

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School Dinners

Age 11 to 14 Short Challenge Level:

Our school dinners offer the same choice each day, and each day I try a new option. How long will it be before I eat the same meal again?

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School Fair Necklaces

Age 5 to 11 Challenge Level:

How many possible necklaces can you find? And how do you know you've found them all?

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Science

Age 11 to 16 Challenge Level:

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Science at University

Why might you wish to study science at university? Read about the views of current students! UNDER DEVELOPMENT

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Scientific Curves

Age 16 to 18 Challenge Level:

Can you sketch these difficult curves, which have uses in mathematical modelling?

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Scientific Mathematics Problem Selection

Age 16 to 18 Challenge Level:

A selection of interesting mathematics challenges which pave the way to the applied mathematics of greatest use at university.

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Scissors, Paper, Rock

Age 5 to 7 Challenge Level:

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

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Scissors, Paper, Rock Chinese Style

Age 5 to 18

Try the Chinese version of this well-known game with a friend. Great to play in the garden or in the park.

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Scooters, Bikes and Trikes

Age 3 to 5

When waiting for a ride on outdoor toys, children can consider which route they might take around the outside area and how long they will spend on their toy.

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Score

Age 11 to 14 Challenge Level:

There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about. . . .

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Scoring with Dice

Age 7 to 11 Challenge Level:

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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Scratch Cards

Age 14 to 16 Challenge Level:

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

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Screen Shot

Age 14 to 16 Challenge Level:

A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees. . . .

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Screwed-up

Age 11 to 14 Challenge Level:

A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?

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Sea Defences

Age 7 to 14 Challenge Level:

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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Sea Level

Age 7 to 11 Challenge Level:

The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?

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Sealed Solution

Age 7 to 11 Challenge Level:

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?